CFD Simulation of Gas-Solid Two-Phase Flow in Pneumatic ... · PDF fileIran. J. Chem. Chem. Eng. Vol. 34, No. 4, 2015 123 CFD Simulation of Gas-Solid Two-Phase Flow in Pneumatic Conveying

Iran. J. Chem. Chem. Eng. Vol. 34, No. 4, 2015

123

CFD Simulation of Gas-Solid Two-Phase Flow

in Pneumatic Conveying of Wheat

Sarrami Foroushani, Ali; Nasr Esfahany, Mohsen*+

Department of Chemical Engineering, Isfahan University of Technology, Isfahan, I.R. IRAN

ABSTRACT: Computational Fluid Dynamics (CFD) simulations of gas-solid flow through

a positive low-pressure pneumatic conveyor were performed using Eulerian-Eulerian framework.

Pressure drop in pneumatic conveying pipelines, creation and destruction of plugs along

the horizontal and vertical pipes, effect of 90° elbows and U-bends on cross-section concentrations,

and rope formation and dispersion were numerically investigated for the wheat particles at

ten different operating conditions. The effects of air inlet velocity and the conveying capacity

on the flow behavior were also discussed. Both parameters played a significant role in the conveying

flow pattern and also the pressure drop. The numerical simulations validated against the experimental

data from literature and also qualitatively compared with trends in experimental data. Excellent

quantitative agreement between experimental and simulated results (±1%) was observed in dense-

phase conveying. For the dilute-phase conveying simulations underestimated the values of pressure

drop by 20%; however, this still falls within the acceptable error ranges reported in the literature.

This study stresses the capability of CFD to explain and predict the behavior of complex gas-solid

conveying systems and to be used productively for investigations in pneumatic conveying of

agricultural and pharmaceutical particles as an aid in the system design..

KEY WORDS: Gas-solid two-phase flow; Pneumatic conveying; Computational fluid dynamics;

U-bend, 90° elbow.

INTRODUCTION

Pneumatic conveying is a commonly used method

for the transport of solid particles such as agricultural seeds,

coal, lime, cement, granular chemicals, and plastic chips

over distances up to several kilometers. When solid

materials are transported in a pneumatic conveying

system two basic modes of flow may be observed,

namely: (1) dilute phase flow or suspension flow

in which the conveying velocity is sufficient to keep

particles suspended while moving through the pipeline,

(2) dense phase flow or non-suspension flow in which

the conveying gas velocity is less than necessary to keep

particles suspended so that majority of particles move

along the pipe while they are not suspended in the

conveying gas [1]. Investigators used different definitions

to distinguish these two flow regimes [2,3]. Since

conveyed materials have great influences on flow modes,

authors such as Geldart, Molerus, Dixon, Pan [4]

provided diagrams giving some indication of different

particle flow modes based on the particle's properties

(e.g., mean diameter, density) [3].

* To whom correspondence should be addressed.

+ E-mail: [email protected]

1021-9986/15/4/123 18/$/3.80

Iran. J. Chem. Chem. Eng. Sarrami Foroushani A. & Nasr Esfahany M. Vol. 34, No. 4, 2015

124

Fig. 1: (a) Plug flow. (b) Dune flow.

Regarding the dense phase pneumatic conveying

of granular materials, flowing through a horizontal pipe,

a wave-like flow has been observed which is shown

in Fig. 1 [1]. In wave-like gas-solid flow, also referred to

dune flow, materials picked up from a moving bed form

a moving plug; then, dropped off toward the moving bed;

having passed a distance along the pipe. If the rolling

waves do not completely fill the pipe cross-section,

the flow will be called dune flow to be more distinct.

However, in the current paper, the wave-like flow

is simply called plug flow. Dense phase flow pneumatic

conveying attracts more interest in industrial applications

due to lower rate of particle attrition and pipeline wear

as well as high particle mass flow rates which leads

to a reduction in need for the conveying gas to convey

a special amount of particles and greater energy

efficiency [1,5]. Since pneumatic conveying is associated with

gas-solid two-phase flow, modeling of such systems is based

on the approaches exist for two-phase flow modeling, i.e.,

Eulerian-Eulerian, Eulerian-Lagrangian and MP-PIC

hybrid models. In Eulerian-Eulerian also referred to

two-fluid approach, each phase is assumed to behave like

a continuum. Separate sets of conservation equations

are used for each phase; therefore, three additional equations

governing the interfacial transfer of mass, momentum,

and energy between phases are required to model

the interactions between phases (jump conditions).

In Eulerian-Lagrangian model also referred to as particle

trajectory approach, solid particles are uncoupled from

the continuous phase and the trajectories of many

individual particles are calculated. In other words,

in particle trajectory model an appropriate form of Newton's

second law plus an accurate solution of the fluid flow

field are the governing equations while in two-fluid

model the governing equations are the two separate sets

of conservation equations plus jump conditions and

closure relations [6]. The third method, MP-PIC, is

a hybrid method where the gas-phase is treated as

a continuum in the Eulerian framework and the solids

are modeled in the Lagrangian framework via tracking

particles. The MP-PIC method employs a fixed Eulerian

grid, and Lagrangian parcels are used to transport mass,

momentum, and energy through this grid in a way that

preserves the identities of the different materials

associated with the particles. The main distinction with

traditional Eulerian-Lagrangian methods is that the

interactions between the particles are calculated on the

Eulerian grid [7]. However, in Eulerian-Lagrangian

approach, since the governing equations should be solved

for each particle in the computational domain, restrictions

of computer memory does not let a full-scale problem

with a large number of particles be solved. For example,

Sakai [8,9] used this method for a dense phase flow

simulation in a horizontal pipe. Due to the computation

restrictions, a short pipe (0.8 m) with relatively small

number of particles ranging from approximately 4,000

to 100,000 was considered. Therefore, application of

Eulerian-Lagrangian approach is restricted to dilute

particle suspensions with limited number of particles

(on the order of 2105 [7]). In contrast, Eulerian-Eulerian

approach is applicable for a wide range of particle

volume fractions (i.e., number of particles).

A review on the recent works in pneumatic conveying

modeling shows that the investigations can be classified

into two main categories, namely, (1) works dedicated

to study the flow characterization in individual piping

components like horizontal pipes, elbows. (2) works

focusing on modeling the flow in a complete set or

a combination of the piping components. Works related

to the first category often considered the flow characteristic

details such as particle volume fraction distribution over

different pipeline cross-sections, fully development

length and the effects of different operating conditions

on such flow characteristics. In contrast, works involved

in the second category considered more general aspects like

pressure drop along the whole pipeline, power

requirement etc. and effect of different operating

conditions on them. In the present study, the pneumatic

Iran. J. Chem. Chem. Eng. CFD Simulation of Gas-Solid Two-Phase Flow … Vol. 34, No. 4, 2015

125

conveying system transporting wheat particles

investigated by Guner [10] is numerically simulated.

The model was first examined for mash independency and

then verified against experimental measurements by

Guner. Then, a detailed CFD analysis of the flow

in different components is presented. In order to identify

stable and unstable conveying regions, pneumatic

conveying phase diagram for this particular system

were constructed based on the simulation results. Dynamic

behavior of gas-solid two-phase flow and contribution of

each system element to the overall pressure drop (energy

consumption) is studied for different components

of the conveyer.

Pneumatic conveying in horizontal and vertical pipes

The dense phase gas-solid two-phase flow in

horizontal pipes is very complicated because of the

gravity acting perpendicular to the flow direction.

The dense phase gas-solid flow is comprised of two layers

moving side by side. In the upper layer, where

the particles are suspended, the fluid-particle forces are

dominate, while in the moving bed at the bottom of the

pipe, with high solid volume fraction, the dominant stress

generation mechanism was more likely to be due to long-

term and multi-particle contacts [11]. Levy [1] employed

two-fluid approach for modeling the horizontal plug flow;

however, for want of the experimental data, the model

was validated by qualitative comparisons.

Pneumatic conveying in elbows and U-bends

Bends are one of the elements in any pneumatic

conveying piping system. They are commonly used

to provide a flexible, compact system of piping. When

gas-solid two-phase flow passes through the bends several

complex phenomena occurs. Formation and dispersion of

ropes of solid particles before and after bends, erosion

at bend outer walls, and an increase in wall-particle and

particle-particle interaction as well as pressure drop are

examples of the mentioned phenomena [12]. Several

investigations have been reported on gas-solid flow

through 90° bend. Huber & Sommerfeld [13], Levy &

Mason [14], Akilli et al. [15], Yilmaz & Levy [16],

studied the effect of a 90° bend on the cross-sectional

particle distribution. Akilli et al. [15] investigated the rope

formation and dispersion in a vertical to horizontal

90° bend using pulverized coal with mean particle diameter

of 50 μm. Yilmaz & Levy [16] studied roping

in a horizontal to vertical 90° elbow while they used 75μm

mean diameter pulverized coal as the solid material.

Kuan et al. [17] did the same using 77 μm diameter glass

particles. McGlinchey et al. [18] used Euler-Euler

approach to numerically investigate pneumatic conveying

in 90° bends with different orientations. Chu & Yu [19]

used 2.8 mm diameter particles to investigate the gas-

solid flow in pneumatic conveying bend. Hidayat et al. [12]

conducted the same investigation for 0.5 mm diameter

particles. El-Behery et al. [20] numerically investigated

flow of gas-solid in a 180° curved duct while using three

different particle sizes (i.e. 60, 100, and 150 μm).

THEORITICAL SECTION

Numerical model

Guner [10] used a positive low pressure conveying

system to experimentally investigate the effect of

different conveying capacities and conveying air

velocities as well as different particles on the pressure

drop along the conveying line and power requirement

for the conveying. The simplified general arrangement

of the pneumatic conveying system is shown in Fig. 2a.

As shown in Fig. 2 a, the system was equipped with

pressure measurement tapping showed by 4 in Fig. 2a.

The difference between the two pressures measured

at the first measurement point and the atmospheric pressure

before the cyclone was reported as the pipeline pressure

drop. A blower was used to deliver air through the system

and the particles to be conveyed are introduced

into the system using an airlock feeder under the hopper.

The two-fluid or Eulerian-Eulerian model was used

to simulate the gas-solid flow.

Geometry and mesh generation

The geometry (i.e., 23 meter long tube) consists of

six parts: two horizontal straight pipes located before and

after the U-bend, 10.25 and 6.1 m long respectively,

a U-bend, a horizontal to vertical elbow, a vertical pipe of

2.4 m long, and a vertical to horizontal elbow. The radius

of curvature of the U-bend is 1.35 m while both elbows have

the same radius of curvature of 0.4 meter. The pipeline

inner diameter is 70.3 mm. Altogether; approximately

183,000 computational unstructured tetrahedral cells

were used for the simulation. The grid was generated

using CFX-mesh and mesh independency was examined


126

Fig. 2: Simplified general arrangement of the pneumatic conveyor: 1, blower; 2, seed hopper and feeder system; 3, conveying

pipeline; 4, pressure drop measurement tapping; 5, cyclone separator. (b) The numerical mesh on the pipeline cross section.

by refining the mesh to approximately 215,000 cells and

comparing the air velocity profiles and the pressure drop

along the pipe for the system in which the air enters with

22.5 m/s and the conveying capacity is 7.5 t/h. It

was found that the difference of the model predicted values

for pressure drop using two mesh schemes was less than

10 % and velocity profiles at different axial positions

were almost the same. The presented simulation results

were obtained using the coarse mesh to include the

computational efficiency. In the near-wall regions, where

velocity gradients are greatest normal to the face,

computationally-efficient meshes require that the

elements have high aspect ratios. Therefore, as shown

if Fig. 2b a three layer inflated boundary (i.e. structured

prismatic cells) with a thickness of the cell adjacent to the

wall of 4% of the pipe diameter and an expansion factor

of 1.2 was employed.

Governing equations

General conservation equations

The conservation of mass equation for phase i is

(i = gas or solid)

i i i i ir r u 0t

(1)

Where ri is the i-th phase volume fraction and

ir 1

The conservation of momentum equation for the gas

phase is (g=gas)

g g g g g g gr u r u ut

(2)

g g g g g g g g gr p r u u r g M

The conservation of momentum equation for the solid

phase is (s = solid)

s s s s s s sr u r u ut

(3)

s s s s s s s s s sr p r u u r g M

Where Mi describes interfacial momentum transfer

(refer to section 2.2.2). The Reynolds stress of phase i

(i=gas or solid), i u u is related to the mean velocity

gradient through Boussinesq hypothesis. Turbulent

kinetic energy and dissipation energy are modeled

employing the realizable k-ε model for the gas

continuous phase [12] while the dispersed phase zero

equation is invoked to model the turbulence in solid

dispersed phase.

Constitutive equations

The following constitutive equations are considered

to close the governing equations set.

The term 𝑀𝑖 in Eqs. (2) and (3) describes the interfacial

drag force acting on phase i due to the presence of the other

phase j [6,12].

i D i jM C u u (4)

Gidaspow drag model which uses the Wen Yu

correlation for rg > 0.8 and Ergun equation for rg < 0.8

was used for dense solid phase [21].

1.65 0.687D g

24C r max 1 0.15Re ,0.44

Re

(5)

g gRe r Re for r 0.8


127

2 2

g g g g i j

D 2sg s

1 r 1 r u u7C 150

4 dr d

(6)

gfor r 0.8

g s i j

g

d u uRe

(7)

The gas phase stress is

Tg g g g g g g g

2r u u r u

3

(8)

The solid phase stress is

Ts s s s s s s s s

2r u u r u

3

(9)

Where is the unit tensor and s is the solids bulk

viscosity and calculated from Lun et al. correlation

presented in equation 13 [21].

The term sp is solid pressure and the kinetic theory

model for solids pressure is similar to the equation of

state for ideal gases, modified to take into account the

particles collisions effect [21].

s s s 0 sp r 1 2 1 e g r (10)

Here, e denotes the coefficient of restitution for solid-

solid collisions, and g0 denotes the radial distribution

function. Gidaspow model for radial distribution function

is [21]

1

1 3

0 s s s,maxg r 0.6 1 r r

(11)

The shear viscosity for solids is expressed by this

equation [21]

2s,col s s s 0

4r d g 1 e

5

(12)

where θ is the granular temperature.

The Lun et al correlation for solids bulk viscosity is

[21]

s s s s 0

4r d g 1 e

3

(13)

Boundary conditions

There are four faces bounding the calculation domain:

(1) the air inlet boundary, where the conveying air leaves

the air supply and enters the pipeline, (2) the particles

inlet boundary, where the particles leave the hopper and

are introduced to the pipeline in the direction

perpendicular to the conveying air direction,

(3) the outlet, where the particles leave the pipeline and

enter the atmospheric cyclone at the end of the line, (4) the

wall boundary. A flow of conveying air was introduced

at the air inlet boundary with a uniform velocity profile

over the entire cross-section; Table 1 shows the air inlet

velocity for different runs. The particles were introduced

with different mass flow rates at the particles inlet

boundary (i.e. 5 t/h and 7.5 t/h). The outlet boundary was

always atmospheric pressure (i.e. traction free boundary

condition). The gravitational direction is downward

in the y-direction. No slip condition was used at the wall

for the gas-phase, and free slip wall function was employed

for solid phase. The free slip condition for the solid phase

assumed that the velocity component parallel to the wall

has a finite value, but the velocity component normal

to the wall and the wall shear stress are both zero.

Solution strategy and convergence

A calculation of multiphase flow using a two-fluid

model for a complex geometry needs an appropriate

numerical strategy to avoid divergence [12]. In this study,

a transient solution strategy with adaptive small time

steps converged to the solutions. In order to judge the

convergence, the residual values of equations -namely

momentum components for each phase, volume fraction

for each phase, turbulence kinetic energy and eddy

dissipation for the continuous phase- has been used; thus,

the solver terminates as the equation residuals calculated

fall below the target residual, while target residual for

the present study has been set to 10-4. The transient solutions

were allowed to continue to reach the steady-state

condition. Because of the wave-like nature of the flow,

steady-state condition is actually not possible in such

systems. Therefore, sustained pressure fluctuations

at the pipeline outlet were taken to be an end point for transient

simulations. The mentioned pressure fluctuations are

due to creation and destruction of plugs within the system.

Detailed description of this issue is presented "RESULTS

AND DISCUSSION" Regarding the system in hand,


128

Table 1: Air inlet velocity at different simulation runs.

Conveying Capacity 5 t/hr 7.5 t/hr

Air Inlet Velocity, m/s Air Inlet Velocity, m/s

Run 1 20.9 20.9

Run 2 22.5 22.5

Run 3 25.31 25.31

Run 4 28.92 28.92

Run 5 32 34

Fig. 3: Comparison between the model predicted pressures

and those measured by Guner [10] for air flow in system (with

no particle load). Each data series is related to a specific inlet

air velocity and includes five points that are related to the five

pressure measurement points.

sustained pressure fluctuations were reached at time

between 15 to 30 seconds depending on the system

conditions (e.g. air inlet velocity and conveying

capacity). All presented results in this work are at t = 30

seconds where the sustained condition is reached.

RESULTS AND DISCUSSION

Validation

To evaluate the performance of the developed model,

comparisons with the experimental data provided by

Guner [10] were carried out. Guner investigated the effect

of different conveying conditions (i.e., conveying air

velocity and conveying capacity) on pressure drop along

a 23 meter long tube. Four types of agricultural seeds

were studied. Measurements for wheat particles with

the mean diameter of 4.35 mm and density of 1325 kg/m3

were used in current study for validation of the model.

Fig. 4: Comparison between the model predicted values for

pressure drop along the 23 m long tube and those measured by

Guner [10] for the system with particle load.

Air only system

Air flow through the 70.3 mm inner diameter tube

with different average velocities ranging from 13 to 33 m/s

was simulated. The predicted results for pressure along

the 23 meter long tube are plotted versus the experimental

data given by Guner [10] in Fig. 3. There is excellent

agreement between the model predicted and experimental

results.

Pneumatic conveying system with particle load

The model predicted results of pressure drop between

the air entrance and exit locations are plotted versus

the experimental data given by Guner [10] for two different

conveying capacities in Fig 4. It is seen from the figure

that current model under-predicts pressure drop along

the whole system for large air inlet velocities in both

conveying capacities. Better agreements are seen for

120

100

80

60

40

20

0

0 20 40 60 80 100 120 0 0.3 0.6 0.9 1.2 1.5 1.8

Pressure, Pa, experiments P, kPa/m, experiment

1.8

1.2

0.6

0

Press

ure, P

a, m

od

el

P

, k

Pa

/m, m

od

el


129

Fig. 5: The model predicted PCC.

lower air inlet velocities. All in all, this can be seen that

the more system's conditions are potential for the dense

phase conveying, i.e., lower inlet air velocities and higher

seeds' loadings, the better agreements is seen. In the field

of dense phase pneumatic conveying, agreement of

models and data are often deemed acceptable if they fall

within the range of ±25% of parity condition [22]; this

can provide convincing evidence that the presented model

is satisfactory.

Phase Diagrams

A phase diagram, also referred to as Pneumatic

Conveying Characteristics (PCC) diagram [23], is usually

a graph of pressure gradient versus superficial air

velocity, based on atmospheric conditions, on which lines

of constant mass flow rate of solids or solid/air mass flow

rate ratio are shown. The PCC diagrams plotted for

conveying 4.35 mm diameter wheat particles at two

different capacities are shown in Fig. 5. As shown

in Fig. 5, by decreasing the air inlet velocity, the pressure

drop slightly decreases for the systems working at high

air inlet flow rates while increases for those working

at lower air inlet flow rates. Studying the pneumatic

conveying characteristics of granular materials

Wypych & Yi [23] provided a typical Pneumatic Conveying

Characteristics (PCC) diagram for granular materials

shown in Fig. 6 which consists of three boundaries A, B,

and C and the curved boundary D delineating

the condition when particles begin to deposit over the bottom

of the pipe line.

Comparing Fig. 6 with CFD predicted data on Fig. 5,

if the selected air mass flow rate is higher than that for

Fig. 6: Typical PCC for granular materials (Wypych & Yi, 2003).

boundary D, the two-phase flow will be in the form

of suspended particles and shows greater energy loss

per unit weight of particles by increasing the air flow rate.

However, when the conveying air velocity decrease

to such extent that is not able to suspend the particles,

the flow mode changes to the dense phase region where

the conveying is in the form of a suspended layer over

a moving bed of deposited particles at the bottom of

the tube. In this region, a further decrease in conveying air

velocity leads to more deposition and migration of

particles from the suspended layer to the moving bed

layer at the bottom and therefore the thickness of

the moving bed layer increases; thus, the area available

for flow of gas is restricted by settled solids. Moreover,

low momentum solid particles jump up from the bed and

decrease the fluid momentum causing extra increase

in pressure drop. According to the boundaries defined by

Wypych & Yi [23] the CFD predictions are placed

between boundaries C and D on Fig. 6.

However, As depicted in Fig. 4, Guner's

measurements show that, the pressure drop over the

whole system increases with the air velocity at the inlet

boundary, which is characteristic of dilute phase

conveying, i.e., beyond the boundary D. To investigate

the CFD simulation’s behavior against further increase

in air inlet velocity, the simulation was performed for two

additional conditions; conveying capacity 7.5 t/h and

conveying air velocity 34 m/s, conveying capacity 5 t/h

and conveying air velocity 32 m/s. It was observed that

the further increase in the conveying air inlet velocity

enables it to suspend the granular materials so that now,

the conditions locate in dilute phase flow zone. Although

1.8

1.6

1.4

1.2 1

0.8

0.6

0.4

0.2 0

20 22 24 26 28 30 32 34 36

Air velocity, m/s

Pip

elin

e p

ress

ure

dro

p k

Pa

/m

Air mass flow rate

Press

ure d

ro

p


130

Fig. 7: Pressure drop fluctuations against time for conveying

air velocity= 28.92 m/s, conveying capacity= 7.5 t/h.

Fig. 8: Model predicted particles volume fraction in the

symmetry plane crossed the conveying pipe axis. Conveying

air velocity= 22.5 m/s, conveying capacity= 7.5 t/h for (a)

the first meter of the conveying pipeline (b) the first 60 cm

of the conveying pipeline.

the CFD simulation under-predicted the dilute phase

conveying Guner's measurements, the simulation predicted

trend shows a very good consistency with other investigators

works on dense phase conveying [2,4,11,22-24]. Wypych

& Yi [23] observed that the transition from suspension

to non-suspension flow is sudden. This sudden change

of flow mode is associated with sudden deposition

of granular materials as the conveying air velocity

decreases and provides an unstable zone in which

prediction of the changes of pressure drop with the

conveying air velocity is not actually possible. As it is

shown on Fig. 5, the simulation predicted data for both

loadings includes an unstable point which is shown by a

different marker. These two points are located

in the unstable transition zone which is related to the

sudden change of flow pattern in pneumatic conveying of

granular materials.

Fluctuations in pneumatic conveying system

Pressure fluctuations in the conveying of solids are

useful for flow pattern identification [25]. For a specified

conveying air inlet velocity, the reduction in available

pipe cross-section due to deposition of particles at the

bottom, causes an increase in air velocity so that it would

be able to suspend more particles and the thickness

of deposited materials (i.e., plug) decreases along the pipe.

The decrease in plug thickness leads to air velocity

(i.e., momentum) decrease and again particles begin to deposit

to make the next rolling dune or plug. The formation and

deformation of plugs cause sustained fluctuations

in pressure drop over the whole pipeline with time for

a specified system with constant air inlet velocity. Levy [1]

studied pressure variations at specific cross sectional

planes along a horizontal tube and depicted

the fluctuations due to plug creations and destruction.

To see the fluctuations in pressure drop as a typical

property of plug flow, pressure drop along the whole

pipeline vs. time is depicted for a specific case in Fig. 7.

The fluctuations have an average period of about

7 seconds, i.e., 0.14 Hz for system in which the conveying air

velocity is 28.92 m/s and the loading is 7.5 t/h which

is decreased to 1.5 seconds as the air inlet velocity

decreases to 22.5 m/s (not shown) for the same amount

of loading. Lee et al [25] also showed the decrease

of fluctuations period as a result of a decrease in conveying

air inlet velocity experimentally.

CFD model results for the horizontal conveying section

Fig. 8 shows the particles volume fraction contour

for the first one meter of the pipeline on the vertical

plane, passing through the pipe axis, dividing the pipe

into two symmetrical sections. As it is shown by Fig. 8,

gravitational forces cause the settling of the particles

at the bottom of the pipe so that the pipe sectional area

can be divided into two layers moving side by side;

the upper layer includes suspended particles while the layer

at the bottom is the moving bed of settled particles.

As mentioned previously, for a specified air inlet

velocity, a portion of pipe cross-section is occupied

by the deposited particles (i.e., the plug) which cause

28500

28400

28300

28200

28100

28000

27900

27800

10 15 20 25 30

Time, s

Press

ure, d

rop

, P

a

0.0 0.2 0.4 0.6 0.8 1.0

Wheat particles volume fraction


131

Fig. 9: Model predicted particles volume fraction at y/D=0.05

at different distances from the air inlet boundary. Conveying

air velocity= 22.5 m/s, conveying capacity= 7.5 t/h.

an increase in conveying air velocity as it passes over

the plug and enables the conveying air to suspend more

particles. Since the conveying air suspends the particles,

it loses momentum which leads to reduction of its

velocity. Reduction of air velocity along the pipe continues

so that some particles deposit again and form the next

plug. Therefore, as shown in Fig. 8, the thickness of the

plug decreases gradually to the point that the next plug

forms. Such behavior provides a wave-like form of creation

and destruction of plugs which could be easily seen

in Fig. 9. In Fig. 9, the particles volume fraction is plotted

along the line located at y/D= 0.05 passing throughout

the pipeline, which shows that the volume fraction on

a specific line in close proximity to the bottom of the pipe

(y/D= 0.05) intermittently decrease and increase due to

formation and destruction of the plugs. When

the particles volume fraction increases to about 0.9

at y/D=0.05, it means that the moving bed depth bordered

y=0.05D. In spite, the decrease in the particles volume

fraction to about 0.6, shows that the y/D=0.05 line

is located in the suspended layer, which means that

the wave is dropped off. As shown in Fig. 8, the particle

volume fraction decreases suddenly at distances about

2.2, 6.2, and 9.2 m from the air inlet and this shows three

successive thin plugs of moving solids (Fig. 9).

Since solid particles settle down at the bottom of

the pipe - resulting in a reduction of the pipe available cross

sectional area, - air velocity increases and more particles

become suspended in the air which leads to gradual

Fig. 10: Normalized air velocity from CFD simulations, at

distances x=2.1, 5.0, 6.4 diameter from the point at which the

particles introduced to the pipeline. Conveying capacity=7.5t/h

and air velocity at the air inlet plane = 22.5 m/s.

decrease of plugs thickness. Levy [1] reported that

the slope at the back of the plug wave is steeper than

the front and CFD model contour shows this in Fig. 8.

Air velocity profiles, plotted along the vertical diameter

of the pipe at distances 2.1, 5.0, and 6.4 diameter from

the point at which the particles introduced to the pipeline,

are depicted in Fig. 10. As it is clearly shown in Fig. 10,

one can divide the velocity profile into two parts

(e.g., plotting velocity profile at x/D= 2.1, division point

can be located at y/D=0.1for conveying of 7.5 t/h of the wheat

particles with the air entering at 22.5 m/s), the upper part

is associated to the suspended upper layer while

the profile at the bottom is associated to the thin moving bed

at the bottom of the conveying pipe. Again, as depicted

in Fig. 10, stepping forward along the pipe

(i.e., increasing x/D), the thickness of the plug decreases

gradually till the next plug raised. Therefore, the division

point located nearer to the bottom of the pipe or even

disappeared if the dunes are discrete from each other.

Fig. 10 also shows that the maximum velocity occurs

closer to the top of the pipe which is attributed to the loss

of gas-phase momentum because of the higher particle

volume fraction near the bottom of the pipe than the top

[13,25,26]. Fully developed air flow is arisen when the

velocity profiles at different distances from the pipe inlet

are the same [25]. Carpinlioglu & Gondugdu [27]

studied the development length of two-phase flow using

wheat particles with mean diameter of 825 μm and

reported that particle shape and size as well as Re have

1

0.8

0.6

0.4

0.2

0

0 1 2 3 4 5 6 7 8 9 10

Z, m

Press

ure, d

rop

, P

a

0 10 20 30 40 50

Air Velocity, m/s

1

0.8

0.6

0.4

0.2

0

y/D


132

Fig. 11: Normalized air velocity from CFD simulations,

at distances x=2.1, 5.0, 6.4 diameter from the point at which

the particles introduced to the pipeline. Conveying capacity=5 t/h


great influences on the development length. They

reported that the development length decreases as Re

increases; and also; the effect of loading ratio on the

development length seems to be negligible. Carpinlioglu

and Gondugdu observed that fully developed flow for

Re=109,000 occurred at 30 < x/D < 40, while for

Re > 120,000, the measured fully developed flow to occur

at x/D < 10. With reference to the Lee et al [25] criterion

for the fully developed flow, i.e., identical velocity profile

at different distances from pipe inlet, velocity profiles

generated by CFD model was plotted for x/D= 2.1, 5.0,

and 6.4 in Fig. 10.

As Fig. 10 shows, the conveying air velocity profiles

are identical for x/D > 5; hence, the model predicted

the conveying of 7.5 t/h of wheat particles using conveying

air with entrance velocity of 22.5 m/s (i.e., Re140,000)

to be fully developed at x/D=5, which is consistent with

the Carpinlioglu and Gondugdu results [27]. The model

predicted fully development length is also qualitatively

consistent with the experimental results provided by

Lee et al. [25]. It was also noted by Carpinlioglu and

Gondugdu that the loading ratio itself seems not to have

much influence on the extent of development length.

To study the effect of loading ratio on the extent of fully

development length, the velocity profiles were plotted for

two different loading ratios, i.e., 5 t/h and 7.5 t/h, while

the conveying air velocity at the pipe inlet was the same

(i.e., 22.5 m/s). Fig. 11 depicts the velocity profiles for

the conveying capacity of 5 t/h. Comparing with Fig. 12

Fig. 12: Normalized air velocity from CFD simulations,

at distances x=5.0, 6.4, 9.2 diameter from the point at which

the particles introduced to the pipeline. Conveying capacity= 7.5 t/h


which was plotted for 7.5 t/h of conveying capacity,

one can see that fully developed flow again occurred

at x/D=5. Therefore, as it was mentioned by Carpinlioglu

and Gondugdu, the conveying capacity does not have any

significant effect on the development length. To study

the effect of Re on the development length and its

consistency with Carpinlioglu and Gondugdu's results, air

velocity profiles were plotted at distances x/D=5.0, 6.4,

and 9.2 (measured from the point at which the particles

introduced to the pipeline) for the same conveying

capacity as that was plotted in Fig. 12 and with a different

air velocity at the air inlet plane that is 20.9 m/s.

As Fig. 12 shows, this time fully development occurred at

x/D=6.4 which is slightly greater than that of case with

air inlet velocity of 22.5 m/s. Hence, as Carpinlioglu &

Gondugdu observed, the development length decreases as

Re increases.

CFD model results for the flow in the bends

Flow in 90° bend

The system simulated in this work includes two 90°

elbows; one is horizontal to vertical and the other is

vertical to horizontal. A sketch of the elbows is presented

in Fig. 13 to show the spatial arrangement of the system.

One of the most important features of gas-solid flow

through bends is roping which is attributed to the

centrifugal force in the elbow, cause the solid particles

to impinge on the outer wall of the bend and forms

a relatively dense phase structure referred to as a rope.

0 5 10 15 20 25 30 35 40

Air Velocity, m/s

1

0.8

0.6

0.4

0.2

0

y/D

1

0.8

0.6

0.4

0.2

0

y/D

0 5 10 15 20 25 30 35 40

Air Velocity, m/s


133

Fig 13: A sketch of the geometry of the end part of the

conveying pipe, i.e., where the two elbows are located.

Fig. 14 shows that passing through the elbow, particles

are conveyed within a rope in a small portion of the pipe

cross-section close to the outer wall due to centrifugal

forces (Fig. 14 b). Moving downstream of the elbow

in vertical direction, the particles in rope region are

accelerated and dispersed in the entire pipe cross-section

(Fig. 14 c). Again, due to centrifugal forces in the elbow,

most of the particles are conveyed within the rope

in a small portion of the pipe cross section close to the top

wall of the horizontal pipe at the exit of the elbow (Fig. 14 d).

Yilmaz & Levy [16] studied the upward flow in a vertical

pneumatic conveying line following a horizontal

to vertical elbow and demonstrated that secondary flows

spread the particles from within the rope and turbulence

creates a more homogeneous distribution of particles.

Therefore, turbulence and secondary flows are both

responsible for dispersion of the rope.

Akilli [15] studied the characteristics of gas-solid

flow in a horizontal pipe following a 90° vertical to

horizontal bend and reported that, while moving along the

horizontal pipe, the rope dispersed and particles

accelerated and spread over the entire cross-section. After

dispersion, larger particles travel in the vicinity of

the bottom wall of the horizontal pipe as a result of gravity.

Therefore, the formation of rope is associated with

the migration of particles toward the outer wall of the elbow

due to centrifugal forces. As the gas-solid flow exits

the elbow the particle rope begin to disperse because

of secondary flows and turbulence [16]. To show

the secondary flows which are responsible for rope

dispersions, the air velocity profiles were plotted at each

elbow's outlet cross-section (i.e., in the direction of r and

θ on cross-sectional planes) in Fig. 15.

Fig. 15a, shows the air velocity profile on a plane

located at the horizontal to vertical elbow outlet while

Fig. 15b shows them on a plane located at the vertical

to horizontal elbow. One can easily see the secondary flows,

which carry the particles over the pipe cross section and

cause the particles to be spread from the rope, on these

two planes; the discontinuities on the lines in these two

plans – at the bottom in Fig. 15 b, and the top in Fig. 15a

– show the accumulated solid and gas phase interface

where the accumulated solid particles and dilute gas

phase separates from each other. Secondary flow lines

can be seen in the gas phase above the interface in Fig. 15a,

and behind the interface in Fig. 15 b. To provide a better

view of rope dispersion, the particles volume fraction

contours on the vertical pipe cross sections at different

distances from the horizontal to vertical elbow's outlet

(i.e., along AA-BB cut in the y direction – see Figs. 13

and 14) are presented in Fig. 16. As depicted in Fig. 16,

the rope started to gradually being dispersed as the conveying

gas flows along the vertical tube and finally dispersed

at distance y/D of about 7 (y = 0.5 m). This observation

is consistent with what Yilmaz & Levy [16] reported.

The effect of the solids conveying capacity on the

particle concentration at the elbow outlet cross-section

(y/D=0) and at different values of y/D along the vertical

tube is studied at a constant conveying air velocity of

22.5 m/s and illustrated in Figs. 17 and 18. Fig. 17 shows

that increasing the conveying capacity caused an increase

in particle volume fraction at different distances from the

elbow's outlet (i.e., y/D). At y/D=0 the particles volume

fraction on the outer wall (z/D=0) is 1 for the both

conveying capacities. However, as the distance from

the elbow's outlet increase to y/D=1 and 2, an increase

in the conveying capacity leads to a greater change

in the particle volume fraction. This continues to y/D=9

at which the majority of particles are suspended in the

rope so that the conveying capacity does a poor job

in affecting the particles volume fraction. At y/D=23,

where the particles are fully suspended, increasing

the conveying capacity slightly affects the particles volume

fractions. Fig. 17 also compares particle volume fraction

profiles, prevailing in the vertical pipe downstream


134

Fig. 14: Predicted solids volume fraction in the symmetry plane of the two 90° elbows at the end of the pipeline, the contour

(a) has been cut to three parts (i.e., b, c, d) to provide a magnified view. Conveying capacity= 7.5 t/h,

conveying air velocity= 22.5 m/sec.

Fig. 15: (a) Secondary flow on the horizontal to vertical elbow's outlet cross-sectional plane. (b) Secondary flow on the pipeline

outlet boundary, i.e., vertical to horizontal elbow.

of the elbow for different solid conveying capacities

at constant conveying air velocity of 22.5 m/s. The particle

rope is denser for high conveying capacity and the rate

of dispersion is higher for lower values of conveying

capacity, which is also consistent with Yilmaz & Levy [16]

experimental results.

Fig. 17 shows that the increase in conveying capacity

does not affect the rope dispersion; however, it causes

the rope to be slightly denser. Similarly, Fig. 18 shows

the effect of conveying air velocity on dispersion of

the particle rope and particle concentration at different planes

of the vertical pipe following the elbow.

The same as what is discussed about Fig. 17, at y/D=0

the particles volume fraction on the outer wall (z/D=0) is

1 for all simulated conveying velocities. However, as the

distance from the elbow's outlet increase to y/D=1 and 2,

an increase in the conveying velocity leads to a greater

change in the particle volume fraction. This continues

to y/D=9 at which the majority of particles are suspended

in the rope so that the conveying velocity does a poor job

in affecting the particles volume fraction. At y/D=23,

where the particles are fully suspended, increasing

the conveying velocity slightly affects the particles volume

fractions. All in all, one can say that for the simulated


135

Fig 16: Predicted particle volume fraction contour for vertical pipe following the first elbow at different distances, y,

from the elbow exit; conveying capacity=7.5 t/h and air velocity=22.5 m/sec.

Fig. 17: Effect of the solids conveying capacity on particle concentration profiles along the pipe diameter

in the direction of z at y/D=0, 1, 2, 9, 23.

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

0.0 0.5 1.0

z/D

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n


136

Fig. 18: Effect of the conveying air velocity at the air inlet cross-section on particle concentration profiles along

the pipe diameter in the direction of z at y/D=0, 1, 2, 9, 23..

velocities, decreasing the conveying air velocity has

almost no effect on the dispersion of the rope while

it causes the rope to be slightly denser. It worth noting that,

as explained in Fig. 16, as flow leaves the horizontal

to vertical elbow and passes through the vertical tube,

the particle rope gradually disperses in the main stream

as y/D increases along the vertical tube.

Flow in U-bend

Fig. 19 shows the effect of horizontal U-bend on the

particles volume fraction distribution over the pipe cross-

section at different angles from the U-bend inlet (θ=0°)

to the U-bend outlet (θ=180°). As shown, particles migrate

near the outer wall due to centrifugal forces and gas

accelerates near the inner wall due to the radial pressure

gradient; it is also shown in Fig. 20, where the air

maximum velocity occurs near the inner wall; In Fig. 20,

the conveying air velocity profiles plotted on a horizontal

plane passing through the pipe axis.

This is to say that, as shown in Fig. 19, the migration

of the solid particles near the outer wall causes the solid

particles to collide with the outer wall, so that they

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n

0.0 0.5 1.0

z/D

0.0 0.5 1.0

z/D

1.0

0.8

0.6

0.4

0.2

0.0

Pa

rti

cle c

on

cen

tra

tio

n


137

Fig. 19: Particles volume fraction contours over the pipeline cross section in the U-bend at different angles.

Conveying air velocity= 22.5 m/s, conveying capacity= 7.5 t/h.

Fig. 20: Velocity profiles at different angles within the

U-bend. Conveying air velocity= 22.5 m/s, conveying

capacity= 7.5 t/h.

decelerate and accumulate on the outer wall of the

U-bend in 0° < θ < 60°. The deceleration and accumulation

of the particles over the outer wall cause the momentum

transfer from gas phase to solid phase to increase; hence,

the air velocity near the outer wall is reduced.

Consequently, the air maximum velocity is shifted to the

outer wall in this region as shown in Fig. 20. For θ > 60°,

although the centrifugal effects exist like the previous

region, the gravitational effects move down the particles

whose momentum reduced due to the collisions.

Therefore, as shown in Fig. 19, comparing θ=30° and

θ=90°, the particles are more concentrated on the outer

wall for θ=30°. Therefore, since some of particles moved

down at the lower bottom of the pipe in θ > 60°,

the effect of the particles integrated on the outer wall

on deceleration of the conveying air is less which cause

the θ=90° velocity profile in Fig. 20, to have a maximum

slightly lower than the maximum in θ=60° velocity

profile. For θ > 90°, all of the particles gradually slide

down at the bottom of the pipe so that the air velocity

near the outer wall in this region is greater than that

in the previous regions and consequently the maximum

velocity is significantly lower than that in previous regions.

The CFD model predicted results in this region are

in a good agreement with what was previously reported

by other investigators [12,20]. After the bend, as discussed

for 90˚ elbows, particles gradually disperse in the

downstream pipe due to turbulence and secondary flow;

this is also shown in Fig. 21, as depicted in the particles

volume fraction contours, the particles left the outer wall

and symmetrically accumulate over the entire bottom part

in the absence of centrifugal forces and radial pressure

0 5 10 15 20 25 30 35 40

Air Velocity, m/s

1

0.8

0.6

0.4

0.2

0

y/D


138

Fig. 21: Particles volume fraction contours after the U-bend in the downstream pipe. (a) pipe cross-sectional contour

immediately after the bend, (b) pipe cross-sectional contour at the distance of 25 cm after the bend, (c) pipe cross-sectional

contour at the distance of 75 cm after the bend.

Fig. 22: Model predicted effect of conveying capacity on the

air velocity profile within the U-bend.

gradient. Effect of particles conveying capacity on the air

velocity profile depicted in Fig. 22. One can see that

the axial velocity for the gas phase increases with

the conveying capacity. El-Behery et al. [20] attributed this

to the momentum transfer from the solid phase to gas

phase because the velocity of solids is greater than that

of gas phase in this region. Effect of the inlet air velocity

on the air velocity profile is depicted in Fig. 23. As shown

the axial velocity in the bend is not highly affected

by the gas inlet velocity which is also reported by

Hidayat & Rasmuson [12]. Considering the effect of conveying

capacity on the pressure drop showed that results

predicted by the model concede other investigators’ [20]

report on the increase of the pressure drop with the

conveying capacity. The increase in pressure drop with

particles conveying capacity is observed in the CFD

results such that the pressure drop over the U-bend

Fig. 23: Model predicted effect of the inlet air velocity on the

air velocity profile within the U-bend.

increases from 6100 Pa to 10000 Pa as conveying

capacity increases from 5 to 7.5 t/h at constant air inlet

velocity of 22.5 m/s.

Contributions of different piping elements to pressure

drop

The prediction of pressure drop along various piping

elements is definitely of great importance for design

purposes. The pressure drop along different parts of the

investigated pneumatic conveyor was studied. It was

observed that horizontal pipe, vertical pipe, vertical

to horizontal elbow, horizontal to vertical elbow and finally

the U-bend are respectively responsible for 65%, 7%,

1.7%, 1.3%, and 25% of the total pressure drop along

the whole 23 m long pipeline. Changing conveying capacity

and conveying air inlet velocity observed to have almost

no effect of the contribution of each element to the total

0 10 20 30 40

Air Velocity, m/s

1

0.8

0.6

0.4

0.2

0

z/D

0 10 20 30 40

Air Velocity, m/s

1

0.8

0.6

0.4

0.2

0

z/D


139

pressure drop. To reach a reliable index to compare the

contribution of elements to the total pressure drop, each

of the above ratios is divided by the ratio of the element

length to the whole pipeline length. It was revealed that

the elements may be arranged from the most to the least

effective as U-bend, vertical pipe, vertical to horizontal

elbow, horizontal to vertical elbow, and horizontal pipe at last.

CONCLUSIONS

CFD calculations using ANSYS-CFX were performed

to investigate the conveying of wheat particles in

a pneumatic conveyor with different piping elements.

Numerical calculation results validated with the

experimental data provided by Guner [10] as well as

qualitative trends in literature. In general, the CFD model

results for pressure drop are in good agreement with

the experimental data. It was observed that better agreements

obtained as the conveying capacity increases and dense-

phase flow occurs. Constructing conveyer phase diagrams

at different operating conditions, the effects of air inlet

velocity and the conveying capacity on the flow behavior

were also discussed. Both parameters played a significant

role in the conveying flow pattern and also the pressure

drop. It was shown that CFD model-based phase

diagrams could be generated during the system design

procedure to assess and predict the optimum operating

condition of the pneumatic conveyer. The overall fairly

good agreement between the CFD model results and

experimental data suggests that CFD can be used

productively for investigations and energy consumption

optimizations in pneumatic conveying of agricultural and

pharmaceutical particles.

Nomenclature

CD Interphase drag coefficient

ds Diameter of solid particle, m

e Solid-solid collision coefficient, energy after

collision and before collision

g0 Radial distribution function

ug Gas-phase velocity, m/s

us Solid-phase velocity m/s

rg Gas-phase volume fraction

λs Solid bulk viscosity, kg/ms

µg Gas viscosity, kg/ms

µs Solid shear viscosity, kg/ms

ρg Gas-phase density, kg/m3

ρs Solid-phase density, kg/m3

θs Granular temperature, m2/s2

Received : Apr. 3, 2013 ; Accepted : Jun. 22, 2015

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